After starting this flurry of debate on whether you should time
average, maybe I should round up by commenting that undoubtably
if you are interested about the average velocity, for instance,
you should as one commentatory pointed out calculate the mean
of the peaks, rather than the peak of the mean (curve). There are
however, times when you wish to obtain a representative curve
against which to compare subsequent/perturbed trials. My original
point was that you should estimate a CURVE (polynomial...) for
each trail and average curves, but not average time-points for
the reasons outlined by Jesus Danen. I am not able to comment on
the Slow F.Transform approach, because having been "stuck in the
fast-lane" I've never considered the SFT approach. If someone would
like to do a tutorial on SFT:FFT differences and the advantages of
SFT for this type of application it would be useful.